# Find integral power of exponent (3 log x)/(x raise to power 4 +1) dx ans with details

$I=\int \frac{\exp ^{3*\log x}}{x^{4}+1} dx$

$I=\int \frac{\exp ^{\log x^{3}}}{x^{4}+1} dx$

$Let \; \; y=\exp ^{\log x^{3}$

$log\; \; y={\log x^{3}\Rightarrow \; \; y=x^{3}$

$I=\int \frac{x^{3}}{x^{4}+1} dx$

$Let\; \; m=x^{4}+1\Rightarrow dm=4*x^{3}\; dx$

$I=\int \frac{1}{4*m} dm$

$I=\frac{1}{4}\log (x^{4}+1)+c \; \; where \; \; c \; \; is \; \; constant$

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